EXERCISE 5.7 1. Write each number in correct scientific notation: a) 7324589000, b) 53000000, c) 0,0000801, d) 158,002 2. Write each number in decimal form: a ) 9,6 * 10^{7} , b) 7,32 * 10^{-4} , c) 1,32 * 10^{-6}, d) 8,063 * 10^{circ} 3. Write the following numbers in ascending order of size: 0,2 *10^{8}, 3,25 *10^{7}, 0,0156 *10^{9} 4. Write 365 billion in scientific notation. 5. Write 45 millionth in scientific notation.

a) In scientific notation, **7324589000** becomes \( 7.324589 \times 10^{9} \). This means we moved the decimal point 9 places to the left. b) For **53000000**, it translates to \( 5.3 \times 10^{7} \). Just shift that decimal point 7 spaces over, and voilà! c) The number **0,0000801** is written as \( 8.01 \times 10^{-5} \) in scientific notation. Here we moved the decimal 5 places to the right. d) The number \( \mathbf{1 5 8 , 0 0 2} \) is represented in scientific notation as \( 1.58002 \times 10^{3} \). The decimal shifted 3 places left. --- a) \( 9.6 \times 10^{7} \) equals **96,000,000** when converted to decimal form. It’s amazing how quickly those zeros can add up! b) \( 7.32 \times 10^{-4} \) converts to **0.000732**. This moves the decimal point four places to the left, showing just how tiny those values can get! c) \( 1.32 \times 10^{-6} \) translates to **0.00000132**. Another small number, perfect for those micro-measurements! d) \( 8.063 \times 10^{0} \) simplifies directly to **8.063** since \( 10^{0} = 1 \). Talk about easy conversions! --- Arranging in ascending order of size: 1. \( 0.0156 \times 10^{1} \) which is **0.156** 2. \( 3.25 \times 10^{7} \) equals **32,500,000** 3. \( 0.2 \times 10^{8} \) gives us **20,000,000** --- To express **365 billion** in scientific notation, it's written as \( 3.65 \times 10^{11} \). Just remember, moving that decimal gives it a whole new look! For **45 millionth**, you write it as \( 4.5 \times 10^{-8} \). A tiny slice of the pie, but just as important in calculations!